just lim_ is treated as ordinary text and \lim_ is the maths way of using limits.
–
Harish KumarMar 30 '12 at 0:51

3

@HarishKumar I believe you are wrong. lim_ is not treated as an ordinary text. lim_ is standalone l, standalone i and standalone m with a following token as a subscript. To make it an ordinary text you have to put \mathit{lim}.
–
yo'Mar 30 '12 at 7:07

1 Answer
1

Without the \, it just treated as three characters l, i, m. This is no different that $xy$ representing a product of two terms x, and y, so $lim$ is a product of three terms: l, i, m. So with $lim_{n\to\infty}$, the subscript is applied to the m term. Perhaps the meaning is more obvious if you write and equivalent statement:

$ l i m_{n\to\infty}$

Note that without the \ the three letters are in italics, representing variables. The operator \lim is not in italics representing an operator.